TCP is the most widely-used transport layer protocol in current Internet, while ATM technology is used to increase the data communication speed at data link layer and network layer. In the TCP-over-ATM architecture, the most significant problems are (i) the partial packet discarding problem, and (ii) the TCP window timeout problem. Several approaches have been proposed to solve the partial packet discard problem and the timeout problem individually, but none of them considered the two problems together. In this paper, we propose an enhanced UBR+ scheme which supports fairness among the TCP connections using UBR+ scheme, and provides protection of damaged VC from the multiple packet losses in the same TCP sliding window. To analyze its performance, we simulate the proposed scheme using OPNET. The simulation results show that the proposed scheme supports fairness, and also increases the throughput by reducing the probability of multiple cell losses in the same TCP window.